I think the division is not the responsibility of Obama, or Trump, or any other politician, but technology.
Not very long ago, our sources of information were somewhat limited. There were three major networks to choose from and one or two newspapers depending on where you lived. For the most part, the majority of people in the U.S. got their news from the same sources and these sources usually reported the same facts in varying amounts of detail.
Generally, major news outlets broadcast news and very little opinion on the 5 o'clock news. Newspapers also printed mostly news, except for one page clearly labeled "Opinion."
Then came a cable news network. It takes a lot of news to fill 24 hours and really, not that much is going on of national importance. Why not fill that extra time with opinions?
Next came other cable news networks and the quest for ratings and advertising revenue.
With more than one news network, each network could be tailored to target a particular audience, an important element of marketing and advertising, creating entire news networks that focus on one target audience and as such give the appearance of being politically biased (Don't believe me? Compare commercials on Fox News and MSNBC.)
Opinion is always more entertaining than news. People like someone giving an opinion that they share. They don't like opinions that they don't share. People like opinions more than facts, even opinions that aren't based on facts. It's much easier to form an opinion by listening to someone else's opinion than compiling facts and forming your own. That begins the rise of Bill O'Reilly and Rachel Maddow.
Enter the Internet. More and more people get their news from the Internet. Now there are not only two or three sides to choose from, but thousands. You can find sources of "news" and opinion that fit exactly with your way of thinking, facts be damned.
In fact, you can can find sources of information that support your opinion and tell you why all other opinions are wrong.
We are no longer all getting the same set of facts and forming reasonable opinions based on those facts. Instead, we are fed custom streams of information that support our beliefs and shun competing beliefs, creating huge divisions.
If that's the case, what's the fix?